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- {{Navigate-First|Book=Linear Algebra|Curr=Systems of linear equations|Next=Matrices}} ...our, time availaibility etc. These constraints can be put in the form of a linear system of equations. ...8 KB (1,206 words) - 11:38, 15 October 2007
- A linear combination of columns n<sub>1</sub>C<sub>1</sub>+n<sub>2</sub>C<sub>2</sub ...the jth column is equal to a<sub>ij</sub>, then if one of the columns is a linear combination of the other columns, then the determinant is equal to 0. ...3 KB (567 words) - 21:29, 9 December 2007
- ==Systems of Linear Equations== A '''linear equation''' in the variables <math>x_1,...,x_n</math>, is an equation that ...11 KB (1,802 words) - 00:41, 29 January 2008
- ...\ldots, \alpha_n</math>, where at least one is different from null, whose linear combinations with the vectors yields the null vector: ...480 bytes (73 words) - 12:43, 20 October 2006
- ...pt in mathematics because many real world phenomena can be approximated by linear models. Unlike a linear function, a linear transformation works on vectors as well as numbers. ...9 KB (1,504 words) - 00:01, 10 December 2007
- Then since the linear combination of two solutions is also a solution (which can be verified dire [[Category:Algebra]] ...797 bytes (130 words) - 22:06, 11 July 2006
- [[Category:Algebra]] ...789 bytes (123 words) - 05:32, 5 May 2007
- Since this is a linear combination of two terms, i is a constant (complex, but still a constant), [[Category:Algebra]] ...1 KB (180 words) - 08:08, 12 August 2007
- ...termined Coefficients as compared to differential equations without linear algebra). [[Category:Algebra]] ...1 KB (216 words) - 22:06, 11 July 2006
- [[Category:Algebra]] ...990 bytes (164 words) - 22:06, 11 July 2006
- *It is linear on the rows of the matrix. .....,''v''<sub>''n''</sub> in '''R'''<sup>''n''</sup> form a [[basis (linear algebra)|basis]] if and only if det(''v''<sub>1</sub>,...,''v''<sub>''n''</sub>) is ...3 KB (458 words) - 13:33, 13 April 2007
- ==Matrices and Linear Transformations== ...ween linear transformations and matrices is very important in the study of linear transformations. ...15 KB (2,557 words) - 22:24, 16 December 2007
- < [[Linear algebra]] === Linear least squares === ...993 bytes (155 words) - 11:35, 7 February 2007
- ; consistent linear system : A linear system with at least one solution. ; equivalent linear systems : Linear systems with the same solution set. ...3 KB (525 words) - 20:32, 20 October 2006
- Vectors can be described mathematically by using [[Algebra/Trigonometry|trigonometry]]. ...only by scalars) to choose some other vector. The set of all vectors under linear combinations of these two vectors form a plane. ...10 KB (1,598 words) - 19:37, 25 September 2006
- As a consequence of Linear Algebra we take the following identity: [[Category:Algebra]] ...1 KB (195 words) - 22:05, 11 July 2006
- [[Category:Algebra textbook pages]] ...3 KB (517 words) - 18:40, 13 April 2007
- ...augmented matrix is very useful when it comes to solving systems, [[Linear Algebra/Matrix Inverses/Finding the Inverse of a Matrix|finding the inverse of a ma ...2 KB (303 words) - 00:40, 27 March 2007
- The general system of linear equations has a solution if the rank of A is equal to the rank of A<sub>1</ ...r equations has a solution only when the last column of A<sub>1</sub> is a linear combination of the other columns. If that is so, then by [[Linear_Algebra/S ...2 KB (336 words) - 02:28, 25 December 2007
- A '''vector space''' is a way of generalizing the concept of a set of [[Algebra/Vectors|vectors]]. For example, the complex number 2+3i can be considered a == Linear Spaces == ...14 KB (2,477 words) - 00:30, 10 December 2007
Page text matches
- {{Algebra}} ...and understand the information presented in the [[Algebra]], and [[Linear Algebra]] books. ...2 KB (214 words) - 22:36, 25 February 2008
- ...("''systems of linear equations in several variables''"), and [[w:algebra|algebra]] ("''study of polynomial equations in one variable''" (though not exclusiv ...|algebraically closed]] and whether <math>k</math> has [[w:Characteristic (algebra)|characteristic]] 0. ...2 KB (372 words) - 19:20, 17 June 2007
- < [[Linear algebra]] === Linear least squares === ...993 bytes (155 words) - 11:35, 7 February 2007
- ===Solutions of systems of linear equations=== A solution of a system of linear equations is a set of numbers for each variable that makes every equation t ...904 bytes (143 words) - 21:14, 28 September 2007
- # [[A-level Mathematics/OCR/FP4/Matrix Algebra|Matrix Algebra]] {{stage short|00%}} # [[A-level Mathematics/OCR/FP4/Solving Linear equations|Solving Linear equations]] {{stage short|00%}} ...932 bytes (111 words) - 20:18, 21 September 2007
- [[Linear algebra]] ==Linear equations== ...5 KB (792 words) - 22:11, 10 June 2006
- ...is: F(X) = ax² + bx + c. Where, ax² is the ''quadratic term'', bx is the ''linear term'' and c is the ''independent term'' or "constant", which does not depe ...will be a maximum and the curve will be concave. If a = 0, then we have a linear function rather than a quadratic function. ...1 KB (253 words) - 02:57, 4 September 2007
- As a consequence of Linear Algebra we take the following identity: [[Category:Algebra]] ...1 KB (195 words) - 22:05, 11 July 2006
- Similarly, a '''Z'''<sub>2</sub>-graded algebra is an algebra A with a direct sum decomposition into an even and an odd part such that th A '''Lie superalgebra''' is a '''Z'''<sub>2</sub>-graded algebra whose product [·, ·], called the '''Lie superbracket''' ...4 KB (624 words) - 09:58, 28 May 2007
- ==== Linear least squares ==== [[Category:Algebra]] ...1,004 bytes (154 words) - 18:38, 13 April 2007
- ...thods/Basic Linear Algebra and Gram-Schmidt Orthogonalization|Basic Linear Algebra and Gram-Schmidt Orthogonalization]] ...n based on linear independent vectors is simpler than computation based on linear dependent vectors. ...4 KB (523 words) - 21:52, 12 October 2007
- {{Navigate-First|Book=Linear Algebra|Curr=Systems of linear equations|Next=Matrices}} ...our, time availaibility etc. These constraints can be put in the form of a linear system of equations. ...8 KB (1,206 words) - 11:38, 15 October 2007
- ...termined Coefficients as compared to differential equations without linear algebra). [[Category:Algebra]] ...1 KB (216 words) - 22:06, 11 July 2006
- ...ns. In the chapter [[Linear Algebra/Systems of Linear Equations|Systems of Linear Equations]] we have used all of these operations, except Scaling. ...operations can be used on all matrices, not just on matrices derived from linear systems. ...2 KB (332 words) - 12:00, 26 December 2007
- Then since the linear combination of two solutions is also a solution (which can be verified dire [[Category:Algebra]] ...797 bytes (130 words) - 22:06, 11 July 2006
- {{nav|Algebra}} '''Solving linear inequalities''' involves finding solutions to expressions where the quantit ...8 KB (1,326 words) - 16:42, 23 September 2007
- ...stant matrix, and other niceties; but when it is otherwise, and thus a non-linear differential equation, the best way to find a solution is by graphical mean [[Category:Algebra]] ...1 KB (165 words) - 22:06, 11 July 2006
- ...tructure of what a matrix represents. If the matrix represents a system of linear equations, these forms allow one to write the solutions to the system. Every Computer Algebra System and most scientific or graphing calculators have commands which prod ...7 KB (1,048 words) - 10:11, 30 August 2007
- ==Matrices and Linear Transformations== ...ween linear transformations and matrices is very important in the study of linear transformations. ...15 KB (2,557 words) - 22:24, 16 December 2007
- ...+ 4</math>), but you may encounter them when doing such things as shaping linear controller data into a curve. ...p://www.mathleague.com/help/algebra/algebra.htm -- A basic introduction to algebra with a focus on turning sentences into equations (you can ignore the sectio ...4 KB (660 words) - 20:54, 17 November 2006